Need some help here

What is the name of your state? OHIO.
Several years ago my grandmother appointed me her Durable Power of Attorney.
She owns a home, where she and my mother reside. (My mother(her daughter) has power of attorney for healthcare.
Her healthcare needs have increased over time and it may be necessary to place her in a nursing home if my mother cannot care for grandma's needs.
I believe the home is still in my grandmother's name, although in lieu of rent, mom has been paying a loan (mortgage) that was taken out against the home to pay other debts. (prior to me being appointed POA).
I have told my mother that if nursing home care is needed, eventually the home will have to be sold to pay for grandma's care (when Medicare runs out) because she cannot hold (the home) an asset and go on medicaid.
Mother does not want to leave the home. Can she keep it from being sold? Will I be responsible for the nursing home costs as POA and put MY home at risk?
and, If a nursing home is needed, can my mother decide which one Grandma is to go to? Can I over-ride the decision?
Thanks for your time,
(OHIO)

Mother does not want to leave the home. Can she keep it from being sold?

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No. You'll have to LEGALLY evict her, though.

Will I be responsible for the nursing home costs as POA and put MY home at risk?

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If you sign the contract incorrectly, yes, you can inadvertently make yourself the guarantor of the nursing homes costs.

can my mother decide which one Grandma is to go to?

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Yes. Your mother is the medical POA.

Can I over-ride the decision?

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You can refuse to sign the contract.

Thanks for your time

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You're welcome.